Since tomatoes are indigenous to America, what would people from what we call Italy today have eaten as a sauce with their pasta?

I'll let you know right from the get-go that some of these recipes might seem, to put it lightly, very odd for modern palettes.

The 13th-14th century Anonymous Venetian gives us a few pasta recipes: recipe XXXVIII for Lenten lasagna, which is... Layers of ground walnuts between the layers, dusted with spices and sugar. Not a sauce, but it also provides a recipe for tortellini/ravioli filling, recipe XLV, includes "fresh strained cheese," "sweet spices, (noted as cloves, ginger, cinnamon, and Bay leaves)" parsley, mint, and sage, mixed in with boiled pork belly. The ravioli are then fried in lard and powdered with more of the spices. Recipe XCIV, labelled as a tart but in effect ravioli, calls for a filling of fish, parsley, marjoram, oil, spices, dates, currants, and pine nuts. A translation can be found here with an original text here

The Anonymous Tuscan Cookery Book of around the same time gives us a sauce recipe (100) of capon broth (chicken broth would be a much easier to make modern equivalent) in which spices, garlic, and almonds are added and reduced to make "white garlic sauce" -- however, it does not indicate what the sauce should be served on. It also includes several other sauces intended specifically for meats, as well as a note on squid ink! Translation can be found here and the original here

Now, there may be other sources that I'm not aware of which include something nearer to what we would consider pasta sauce, but it seems like their conception of how pasta should be prepared/eaten was somewhat different from our own today.